How do you graph #y - 4 < x - 6#?

1 Answer
Apr 4, 2015

First of all, let's study where the equation holds: you have
#y-4=x-6 \iff y=x-2#.
This is the equation of a line, which you can easily graph. If you think about it, the graph of a function is the set of the points which satisfy the relation #y=f(x)#; but we are looking for the points which satisfy the relation #y < f(x)#.

You can see that the two requests are strongly related: if the graph of the line is the set of points in which #y=x-2# holds, the set of points in which #y< x-2# holds is the part of the plan below the graph, as you can see:

graph{y< x-2 [-10, 10, -5, 5]}